Precoding Designs in Non-Regenerative MIMO Two-Way Relay Systems for Maximizing Weighted Sum Energy Efficiencies

In this paper, we investigate the energy efficient optimization for non-regenerative multiple-input- multiple-output (MIMO) Two-Way Relay (TWR) network. Contrary to existing energy efficiency (EE) optimal precoding designs, we maximize the weighted sum per- source energy efficiencies (WSEE) subject to the maximum transmit power constraints of sources and relay, such that different EE requirements from the sources can be investigated. The resulting optimization problem is a non-convex sum of ratios problem. To address this issue, we first reformulate the objective as a more tractable parametric subtraction form by introducing some auxiliary variables. Then we develop an efficient block coordinate decent method to solve the equivalent problem with respect to the individual optimization variable. It is shown that the proposed iterative algorithm is guaranteed to converge.